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discoveries- he had made as a boy of seventeen, Part I of A
Theory of Systems of Rays, the great classic which does for
optics what Lagrange's Mecanique anatytique does for mechan-
ics and which, in Hamilton's own hands, was to be extended to
dynamic*, putting that fundamental science in what is perhaps
its ultimate, perfect form.
The techniques which Hamilton introduced into applied
mathematics in this, his first masterpiece, are to-day indispen-
^abie in mathematical physics, and it is the aim of many
workers in particular branches of theoretical physics to sum up
tne whole of a theory in a Hamiltonian principle. This magnifi-
cent work is that which caused Jacobi, fourteen years later at
the British Association meeting at Manchester in 1842, to assert
that "Hamilton is the Lagrange of your country' - (meaning of
the English-speaking race). As Hamilton himself took great
pains to describe the essence of his new methods in terms com-
prehensible to non-specialists, we shall quote from his own
abstract presented to the Royal Irish Academy on 23 April
"A Ray, in Optics, is to be considered here as a straight or
bent or curved line, along which light is propagated; and a
System of Rays as a collection or aggregate of such lines, con-
nected by some common bond, some similarity of origin or
production, in short some optical unity. Thus the rays which
diverge from a luminous point compose one optical system, and,
after they have been reflected at a mirror, they compose
another. To investigate the geometrical relations of the rays of
a system of which we know (as in these simple cases) the optical
origin and history, to inquire how they are disposed among
themselves, how they diverge or converge, or are parallel, what
surfaces or curves they touch or cut, and at what angles of
section, how they can be combined hi partial pencils, and how
each ray in particular can be determined and distinguished
from every other, is to study that System of Rays. And to
generalize this study of one system so as to become able to pass,
without change of plan, to the study of other systems, to assign
general rules and a general method whereby these separate
optical arrangements may be connected and harmonized to-